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Unformatted text preview: determine the most ecient way to combine these legs into ight schedules. The starting time for ight i is a i and the nishing time is b i . The plane requires r ij hours to return from the destination of ight leg i to the start (origin) point of ight leg j . Suggest a way to solve this problem using ow. 3. [6.40] Given a directed graph G = ( N, A ) with upper bounds on the ow u ij which are integer, and nodes s, t N , we know that there is a max ow from s to t that is integer. Suppose that instead, a helpful friend gives us a max ow x ij where some of the ows are noninteger. Show how to convert this ow into an integer maximum ow. The running time of your algorithm should be O ( mf ) wher m is the number of arcs and f is the number of arcs with fractional (noninteger) ow on them. Hint: Send ows along cycles....
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- Fall '08